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<p>We provide a proof of the BRST Noether 1.5th theorem, conjectured in [<a href="https://doi.org/10.1007/JHEP10(2024)055"><i>JHEP</i></a><a href="https://doi.org/10.1007/JHEP10(2024)055"><b>10</b> (2024) 055</a>], for a broad class of rank-1 BV theories including supergravity and 2-form gauge theories. The theorem asserts that the BRST Noether current of any BRST invariant gauge fixed Lagrangian decomposes on-shell into a sum of a BRST-exact term and a corner term that defines Noether charges. This extends the holographic consequences of Noether’s second theorem to gauge fixed theories and, in particular, offers a universal gauge independent Lagrangian derivation of the invariance of the <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">S</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{S} \)</EquationSource> </InlineEquation>-matrix under asymptotic symmetries. Furthermore, we show that these corner Noether charges are inherently non-integrable. To address this non-integrability, we introduce a novel charge bracket that accounts for potential symplectic flux and anomalies, providing an honest canonical representation of the asymptotic symmetry algebra. We also highlight a general origin of a BRST cocycle associated with asymptotic symmetries.</p>

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BRST Noether theorem and corner charge bracket

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月5日

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  • Laurent Baulieu,
  • Tom Wetzstein,
  • Siye Wu

摘要

We provide a proof of the BRST Noether 1.5th theorem, conjectured in [JHEP10 (2024) 055], for a broad class of rank-1 BV theories including supergravity and 2-form gauge theories. The theorem asserts that the BRST Noether current of any BRST invariant gauge fixed Lagrangian decomposes on-shell into a sum of a BRST-exact term and a corner term that defines Noether charges. This extends the holographic consequences of Noether’s second theorem to gauge fixed theories and, in particular, offers a universal gauge independent Lagrangian derivation of the invariance of the S \( \mathcal{S} \) -matrix under asymptotic symmetries. Furthermore, we show that these corner Noether charges are inherently non-integrable. To address this non-integrability, we introduce a novel charge bracket that accounts for potential symplectic flux and anomalies, providing an honest canonical representation of the asymptotic symmetry algebra. We also highlight a general origin of a BRST cocycle associated with asymptotic symmetries.